Question 1

At what location does an artificial Earth satellite in elliptical orbit have its lowest speed?
A) nearest the Earth
B) farthest from the Earth
C) between Earth and Moon
D) between Earth and Sun

Accepted Answer

According to Kepler's laws of planetary motion, the speed of a satellite in an elliptical orbit varies as it moves around its orbit, being fastest at the closest point to the Earth (perigee) and slowest at the farthest point (apogee). Therefore, the lowest speed of an artificial Earth satellite in elliptical orbit would be at its farthest point from the Earth, which is answer choice B.

Question 2

For any object orbiting the Sun, Kepler's Law may be written T² = kr³. If T is measured in years and r in units of the Earth's distance from the Sun, then k = 1. What, therefore, is the time (in years) for Jupiter to orbit the Sun if its mean radius from the Sun is 5.2 times the Earth's distance from the Sun? A) 5.2 years B) 6.0 years C) 12 years D) 16 years

Accepted Answer

According to Kepler's Third Law, T² = r³ when k = 1. For Jupiter, r = 5.2, so T² = 5.2³ = 140.608. Solving for T gives T ≈ √140.608 ≈ 11.85, which rounds to 12 years.

Question 3

What is (are) the location(s) of the low tide(s) on Earth caused by the gravitation of the Moon? Give the location(s) relative to the line through the Earth's and Moon's centers, line EM.
A) the point on EM on the Earth's surface nearest to the Moon
B) the point on EM on the Earth's surface farthest from the Moon
C) the points on the Earth's surface perpendicular to EM at the Earth's center
D) the points on EM on the Earth's surface nearest to and farthest from the Moon

Accepted Answer

Low tides occur at the points on the Earth's surface that are perpendicular to the line through the Earth's and Moon's centers (line EM), due to the gravitational pull of the Moon causing water to be drawn away from these areas.

Question 4

An asteroid in orbit about the Sun has a linear speed of 4 km/s when at a distance of closest approach d from the sun. What is its linear speed when it is at its greatest distance from the sun, a distance 4d?
A) 1 km/s
B) 2 km/s
C) 8 km/s
D) 16 km/s

Accepted Answer

The answer of An asteroid in orbit about the Sun...

Question 5

Of the known planets in our solar system, the innermost is Mercury. When compared to the other planets in the system, Mercury has:
A) the greatest centripetal acceleration.
B) the greatest period of revolution.
C) the smallest speed.
D) none of the above properties.

Accepted Answer

Mercury, being the closest planet to the Sun, experiences the greatest centripetal acceleration due to its proximity and the gravitational pull from the Sun.

Question 6

An asteroid has a perihelion (the orbit's closest approach to the Sun) of 2.5 AU and a period of revolution of 8.0 y. What is its greatest distance from the Sun (its aphelion)? (Hint: For an elliptical orbit, the effective radius of the orbit is half the sum of the nearest distance to the Sun and the greatest distance from the Sun.)
A) 8.0 AU
B) 6.5 AU
C) 5.5 AU
D) 2.5 AU

Accepted Answer

The semi-major axis (a) of the orbit can be found using Kepler's third law: a^3 = T^2, where T is the period in years. Here, a^3 = 8^2 = 64, so a = 4 AU. The semi-major axis is the average of the perihelion (2.5 AU) and aphelion (A). Thus, (2.5 + A)/2 = 4, solving gives A = 5.5 AU.

Question 7

An observation satellite for mapping purposes is placed in a low Earth orbit. In order to see the whole surface of the Earth, which would be the preferred orbit?
A) an equatorial orbit
B) a polar orbit
C) an orbit inclined 45° to the equator
D) It doesn't matter since the Earth turns completely every 24 hours.

Accepted Answer

A polar orbit would allow the satellite to see the entire surface of the Earth as it rotates underneath the orbit. An equatorial orbit would only provide a view of a narrow strip along the equator and an orbit inclined at 45° would provide a view of more of the Earth's surface, but not the entire globe. The Earth's rotation does not affect the need for the satellite to be in a polar orbit to see the entire surface.

Question 8

When the Earth's and Moon's centers are 59 Earth radii apart, what is the ratio of the lunar gravitational force on a 2-kg mass at the point on the Earth nearest to the Moon to the lunar gravitational force on a 2-kg mass at the point on the Earth farthest from the Moon? A) 118/59 B) (58/60)² C) (60/58)² D) The value is not given.

Accepted Answer

The lunar gravitational force on a mass is inversely proportional to the square of the distance between the mass and the Moon's center. The distance between the point on the Earth nearest to the Moon and the Moon's center is 59 Earth radii, while the distance between the point on the Earth farthest from the Moon and the Moon's center is 61 Earth radii. Therefore, the ratio of the lunar gravitational force on a 2-kg mass at the point on the Earth nearest to the Moon to the lunar gravitational force on a 2-kg mass at the point on the Earth farthest from the Moon is (60/58)².

Question 9

An artificial Earth satellite in an elliptical orbit has its greatest centripetal acceleration when it is at what location?
A) nearest the Earth
B) farthest from the Earth
C) between Earth and Moon
D) between Earth and Sun

Accepted Answer

Centripetal acceleration is given by a = v^2/r, where v is the velocity of the object and r is its distance from the center of the gravitational force. As the satellite is in an elliptical orbit, its distance from the Earth varies throughout its orbit. At the point closest to the Earth (called perigee), the satellite has the highest velocity and the smallest distance from the center of the Earth, resulting in the greatest centripetal acceleration.

Question 10

Two satellites are monitored as they orbit the Earth; satellite X is four times as far from the Earth's center as is satellite Y. From Kepler's third law one may conclude that the period of revolution of X is what factor times that of Y?
A) 1/2
B) 2.0
C) 8.0
D) 22.6

Accepted Answer

Kepler's third law states that the square of the period of revolution of a planet (or satellite) is proportional to the cube of its average distance from the sun (or Earth). Let Y be at a distance of r from the Earth's center, then X is at a distance of 4r from the Earth's center. So, (T_x)^2:(T_y)^2 = (4r)^3:r^3 = 64:1. Taking the square root of both sides, we get (T_x):(T_y) = 8:1. Therefore, the period of revolution of X is 8 times that of Y.

Question 11

According to Kepler's laws, Halley's Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse. What is it that Kepler's laws indicate is at the other focus of the ellipse?
A) nothing
B) the Earth
C) The comet itself passes through the other focus.
D) The tail of the comet stays at the other focus.

Accepted Answer

According to Kepler's first law, each planet or comet orbits the Sun in an ellipse with the Sun at one focus and nothing at the other focus.

Question 12

When it comes to tides, high and low, what is the usual situation on the ocean's coast?
A) one high tide or one low tide a day
B) one high tide and one low tide a day
C) two high tides and two low tides a day
D) high tides in the day and low at night

Accepted Answer

Most coastal areas experience two high tides and two low tides each day due to the gravitational pull of the moon and the sun on Earth's oceans.

Question 13

Which of the following best describes the property of the period of orbital revolution for an Earth satellite?
A) greater when the orbital radius is smaller
B) greater when the orbital radius is larger
C) independent of the orbital radius
D) determined mainly by the satellite's mass

Accepted Answer

The period of orbital revolution for an Earth satellite is directly proportional to the radius of its orbit. As the radius increases, the period also increases. This can be explained by Kepler's third law, which states that the square of the period of an orbit is proportional to the cube of the semi-major axis of the orbit. The mass of the satellite does not play a significant role in determining the period of its orbit.

Question 14

A double star system with each star having the mass of the Sun has an orbital period of 1 year. A second double star system, also with each star having the mass of the Sun, has an orbital period of 8 years. If the separation of the stars in the first system is d and the orbits in both cases are circular, what is the separation of the stars in the second system?
A) 0.5d
B) 2d
C) 4d
D) 8d

Accepted Answer

From Kepler's Third Law, we know that $T^2 \propto a^3$, where T is the orbital period and a is the semi-major axis of the orbit. Since both systems have masses of the Sun, this proportionality relation can be written as $T^2 \propto d^3$.

Using this relation for the first system, we have $1^2 \propto d^3$, which gives $d = 1$.

For the second system, we know that $8^2 \propto a^3$. Since the mass of the stars is the same as the first system, we have $a = kd$ for some constant k. Plugging this into the proportionality relation and solving for k gives $k = 2$. Therefore, the separation of the stars in the second system is $a = 2d \cdot 2 = 4d$.

Therefore, the best choice is C) 4d.

Question 15

In order for a satellite to be geosynchronous, its orbit must:
A) go over the North and South Poles.
B) be over the equator.
C) be over a single longitude.
D) emit television signals.

Accepted Answer

A geosynchronous satellite must have an orbit that is over the equator and maintains the same orbital speed as the rotation of the Earth, allowing it to appear stationary relative to a fixed position on the ground. The other options are not necessary for a satellite to be geosynchronous.

Quiz 5: Circular Motion and Gravitation

At what location does an artificial Earth satellite in elliptical orbit have its lowest speed?

What is (are) the location(s) of the low tide(s) on Earth caused by the gravitation of the Moon? Give the location(s) relative to the line through the Earth's and Moon's centers, line EM.

An asteroid in orbit about the Sun has a linear speed of 4 km/s when at a distance of closest approach d from the sun. What is its linear speed when it is at its greatest distance from the sun, a distance 4d?

Of the known planets in our solar system, the innermost is Mercury. When compared to the other planets in the system, Mercury has:

An observation satellite for mapping purposes is placed in a low Earth orbit. In order to see the whole surface of the Earth, which would be the preferred orbit?

When the Earth's and Moon's centers are 59 Earth radii apart, what is the ratio of the lunar gravitational force on a 2-kg mass at the point on the Earth nearest to the Moon to the lunar gravitational force on a 2-kg mass at the point on the Earth farthest from the Moon?

An artificial Earth satellite in an elliptical orbit has its greatest centripetal acceleration when it is at what location?

Two satellites are monitored as they orbit the Earth; satellite X is four times as far from the Earth's center as is satellite Y. From Kepler's third law one may conclude that the period of revolution of X is what factor times that of Y?

According to Kepler's laws, Halley's Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse. What is it that Kepler's laws indicate is at the other focus of the ellipse?

When it comes to tides, high and low, what is the usual situation on the ocean's coast?

Which of the following best describes the property of the period of orbital revolution for an Earth satellite?

In order for a satellite to be geosynchronous, its orbit must: